TSTP Solution File: NUM852+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : NUM852+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:42:22 EDT 2023
% Result : Theorem 3.19s 1.72s
% Output : Refutation 3.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 29
% Syntax : Number of formulae : 51 ( 16 unt; 9 typ; 0 def)
% Number of atoms : 74 ( 30 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 294 ( 14 ~; 10 |; 2 &; 248 @)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 78 ( 0 ^; 72 !; 6 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_type,type,
greater: $i > $i > $o ).
thf(vmul_type,type,
vmul: $i > $i > $i ).
thf(vd481_type,type,
vd481: $i ).
thf(vd469_type,type,
vd469: $i ).
thf(vd480_type,type,
vd480: $i ).
thf(less_type,type,
less: $i > $i > $o ).
thf(vplus_type,type,
vplus: $i > $i > $i ).
thf(vskolem9_type,type,
vskolem9: $i > $i > $i ).
thf(vsucc_type,type,
vsucc: $i > $i ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( ( vmul @ A @ vd469 )
= ( vmul @ ( vplus @ B @ ( vskolem9 @ A @ B ) ) @ vd469 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 2)') ).
thf(42,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( ( vmul @ A @ vd469 )
= ( vmul @ ( vplus @ B @ ( vskolem9 @ A @ B ) ) @ vd469 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( A
= ( vplus @ B @ ( vskolem9 @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 3)') ).
thf(52,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( A
= ( vplus @ B @ ( vskolem9 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
thf(57,plain,
! [A: $i,B: $i] :
( ( less @ A @ B )
=> ( greater @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
thf(74,plain,
! [A: $i,B: $i] :
( ~ ( greater @ A @ B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( vmul @ A @ ( vplus @ B @ C ) )
= ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).
thf(77,plain,
! [A: $i,B: $i,C: $i] :
( ( vmul @ A @ ( vplus @ B @ C ) )
= ( vplus @ ( vmul @ A @ B ) @ ( vmul @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
thf(71,plain,
! [A: $i,B: $i] :
( ( vmul @ A @ B )
= ( vmul @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,axiom,
less @ vd480 @ vd481,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(antec(304), 482, 0)') ).
thf(76,plain,
less @ vd480 @ vd481,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( vmul @ ( vmul @ A @ B ) @ C )
= ( vmul @ A @ ( vmul @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(290, 0), 0)') ).
thf(80,plain,
! [A: $i,B: $i,C: $i] :
( ( vmul @ ( vmul @ A @ B ) @ C )
= ( vmul @ A @ ( vmul @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( ( vmul @ ( vplus @ B @ ( vskolem9 @ A @ B ) ) @ vd469 )
= ( vplus @ ( vmul @ B @ vd469 ) @ ( vmul @ ( vskolem9 @ A @ B ) @ vd469 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 1)') ).
thf(67,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( ( vmul @ ( vplus @ B @ ( vskolem9 @ A @ B ) ) @ vd469 )
= ( vplus @ ( vmul @ B @ vd469 ) @ ( vmul @ ( vskolem9 @ A @ B ) @ vd469 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 1)') ).
thf(30,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( greater @ ( vplus @ ( vmul @ B @ vd469 ) @ ( vmul @ ( vskolem9 @ A @ B ) @ vd469 ) ) @ ( vmul @ B @ vd469 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(302, 0), 0)') ).
thf(62,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( greater @ ( vplus @ ( vmul @ B @ vd469 ) @ ( vmul @ ( vskolem9 @ A @ B ) @ vd469 ) ) @ ( vmul @ B @ vd469 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( ( vmul @ A @ vd469 )
= ( vmul @ B @ vd469 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(303, 0), 0)') ).
thf(38,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( ( vmul @ A @ vd469 )
= ( vmul @ B @ vd469 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,axiom,
greater @ vd481 @ vd480,
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq(304)), 483, 0)') ).
thf(70,plain,
greater @ vd481 @ vd480,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 3)') ).
thf(34,plain,
! [A: $i,B: $i] :
( ( A != B )
| ~ ( greater @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( greater @ B @ A )
<=> ? [C: $i] :
( B
= ( vplus @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(45,plain,
! [A: $i,B: $i] :
( ( ( greater @ B @ A )
=> ? [C: $i] :
( B
= ( vplus @ A @ C ) ) )
& ( ? [C: $i] :
( B
= ( vplus @ A @ C ) )
=> ( greater @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
thf(64,plain,
! [A: $i,B: $i] :
( ( A = B )
| ( greater @ A @ B )
| ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)') ).
thf(2,negated_conjecture,
~ ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ( greater @ ( vmul @ vd481 @ vd469 ) @ ( vmul @ vd480 @ vd469 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( vmul @ ( vsucc @ A ) @ B )
= ( vplus @ ( vmul @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
thf(59,plain,
! [A: $i,B: $i] :
( ( vmul @ ( vsucc @ A ) @ B )
= ( vplus @ ( vmul @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
thf(55,plain,
! [A: $i,B: $i] :
( ( greater @ A @ B )
=> ( less @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( less @ B @ A )
<=> ? [C: $i] :
( A
= ( vplus @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(23,plain,
! [A: $i,B: $i] :
( ( ( less @ B @ A )
=> ? [C: $i] :
( A
= ( vplus @ B @ C ) ) )
& ( ? [C: $i] :
( A
= ( vplus @ B @ C ) )
=> ( less @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(83,plain,
$false,
inference(e,[status(thm)],[42,52,57,74,77,71,76,80,67,30,62,38,70,34,45,64,22,59,55,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM852+2 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n013.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 16:50:07 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.96/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.31/0.96 % [INFO] Parsing done (118ms).
% 1.31/0.97 % [INFO] Running in sequential loop mode.
% 1.69/1.16 % [INFO] eprover registered as external prover.
% 1.69/1.16 % [INFO] cvc4 registered as external prover.
% 1.69/1.16 % [INFO] Scanning for conjecture ...
% 1.77/1.21 % [INFO] Found a conjecture and 19 axioms. Running axiom selection ...
% 1.95/1.25 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 1.95/1.28 % [INFO] Problem is first-order (TPTP FOF).
% 1.95/1.28 % [INFO] Type checking passed.
% 1.95/1.28 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.19/1.71 % External prover 'e' found a proof!
% 3.19/1.71 % [INFO] Killing All external provers ...
% 3.19/1.71 % Time passed: 1188ms (effective reasoning time: 738ms)
% 3.19/1.71 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.19/1.71 % Axioms used in derivation (19): def(cond(conseq(axiom(3)), 11), 1), holds(antec(304), 482, 0), ass(cond(302, 0), 2), ass(cond(147, 0), 0), ass(cond(281, 0), 0), ass(cond(302, 0), 1), ass(cond(261, 0), 0), ass(cond(goal(130), 0), 2), ass(cond(140, 0), 0), def(cond(conseq(axiom(3)), 12), 1), ass(cond(302, 0), 0), ass(cond(goal(130), 0), 1), ass(cond(302, 0), 3), ass(cond(goal(130), 0), 0), ass(cond(goal(130), 0), 3), ass(cond(270, 0), 0), holds(conseq_conjunct1(conseq(304)), 483, 0), ass(cond(290, 0), 0), ass(cond(303, 0), 0)
% 3.19/1.71 % No. of inferences in proof: 42
% 3.19/1.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1188 ms resp. 738 ms w/o parsing
% 3.19/1.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.19/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------